Don't scrub the thing, tissue and lens cleaner or ammonia solution.
Don't press the tissue flat, make a ball or wad about 3/16-1/4" and use a circular motion.
It's going to take several applications, just take it easy.
Older lenses have much softer internal coatings than newer, careful anyhow.

BTW I've successfully removed inner coatings myself. intentionally(cough), right